Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	50×	body	1280	valid
6.0ms	134×	body	80	valid
5.0ms	39×	body	640	valid
2.0ms	23×	body	320	valid
1.0ms	10×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
75.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(/ x (+ x 1.0))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify206.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune725.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
28.9b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ 1 (+ x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series200.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (+ x 1.0) (- x 1.0))
22.0ms	(/ 1 (+ x 1.0))
136.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify40.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	352	622
1	1229	566
2	5001	540

prune180.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
17.0b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
44×	`associate-*r/`
43×	`add-cube-cbrt`
37×	`prod-diff`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
24×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate--l+`
20×	`frac-times` `flip3--` `flip--`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 198

Calls

4 calls:

11.0ms	(* x (- x 1.0))
16.0ms	(* (+ x 1.0) (+ x 1.0))
27.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
12.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* x (- x 1.0))
15.0ms	(* (+ x 1.0) (+ x 1.0))
52.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
37.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	906	2204
1	5002	1888

prune445.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
13.9b	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`difference-of-squares`
10×	`associate-/l*`
5×	`neg-mul-1`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `flip3--` `fma-def` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 88

Calls

2 calls:

3.0ms	(+ (* 3.0 x) 1.0)
17.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

series83.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* 3.0 x) 1.0)
52.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	410	971
1	1643	910
2	5001	900

prune193.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	14	6
2	14	6

end0.0ms

sample818.0ms

Algorithm

intervals

Results

275.0ms	1693×	body	1280	valid
190.0ms	4142×	body	80	valid
160.0ms	1231×	body	640	valid
67.0ms	627×	body	320	valid
24.0ms	307×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6